If $2\sin^3x+\sin2x\cos x+4\sin x-4=0$ has exactly $3$ solutions in the interval $\left[0,\dfrac{n\pi}{2}\right],,n\in\mathbb N$, then the roots of the equation $x^2+nx+(n-3)=0$ belong to:

1

If $z=x+iy$ with $xy\ne0$ satisfies $z^{2}+i\overline{z}=0$, then $|z^{2}|$ equals:

Topic: JEE Main 2024 (30 January Morning Shift)

2

Let $y=y(x)$ be the solution of the differential equation $\sec x,dy+{2(1-x)\tan x+x(2-x)},dx=0$ with $y(0)=2$. Then $y…

Topic: JEE Main 2024 (30 January Morning Shift)

3

Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $ABCD$. If the diagonal $\overrightarrow{BD}= \…

Topic: JEE Main 2024 (30 January Morning Shift)

4

Two integers $x$ and $y$ are chosen with replacement from the set ${0,1,2,3,\ldots,10}$. Then the probability that $|x-…

Topic: JEE Main 2024 (30 January Morning Shift)

5

If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity …

Topic: JEE Main 2024 (30 January Morning Shift)

6

Let M denote the median of the following frequency distributionThen 20M is equal to :

Topic: JEE Main 2024 (30 January Morning Shift)

7

Let $f:[-\tfrac{\pi}{2}, \tfrac{\pi}{2}] \to \mathbb{R}$ be a differentiable function such that $f(0)=\tfrac{1}{2}$. If…

Topic: JEE Main 2024 (30 January Morning Shift)

8

Consider the system of linear equations $x + y + z = 4\mu,\quad x + 2y + 2\lambda z = 10\mu,\quad x + 3y + 4\lambda^2 z…

Topic: JEE Main 2024 (30 January Morning Shift)

9

A line passing through the point \(A(9,0)\) makes an angle of \(30^\circ\) with the positive direction of the \(x\)-axi…

Topic: JEE Main 2024 (30 January Morning Shift)

10

Let $(\alpha,\beta,\gamma)$ be the foot of the perpendicular from the point $(1,2,3)$ on the line \[ \frac{x+3}{5}=\fra…

Topic: JEE Main 2024 (30 January Morning Shift)

1

If the domain of the function $f(x)=\cos^{-1}!\left(\dfrac{2-|x|}{4}\right)+{\log_e(3-x)}^{-1}$ is $[-\alpha,\beta)-{\g…

Topic: JEE Main 2024 (30 January Morning Shift)

2

Let $S_n$ denote the sum of first $n$ terms of an arithmetic progression. If $S_{20}=790$ and $S_{10}=145$, then $S_{15…

Topic: JEE Main 2024 (30 January Morning Shift)

3

The area (in square units) of the region bounded by the parabola $y^{2}=4(x-2)$ and the line $y=2x-8$ is:

Topic: JEE Main 2024 (30 January Morning Shift)

4

Let $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=\dfrac{x}{(1+2x^{4})^{1/4}}$, and $g(x)=f(f(f(f(x))))$. Then $18\di…

Topic: JEE Main 2024 (30 January Morning Shift)

5

Let $a,b$ be distinct positive reals. The $11^{\text{th}}$ term of a GP with first term $a$ and third term $b$ equals t…

Topic: JEE Main 2024 (30 January Morning Shift)